Abductive Reasoning in Fuzzy Logic Explored

Katsumi Inoue and Daniil Kozhemiachenko published their study on September 17, 2026 in the Journal of Artificial Intelligence Research (JAIR), presenting a novel approach to abductive reasoning within contexts that involve fuzzy statements such as “the lift is heavily loaded” or “it is cold outside.” ¹

The authors note that observations and explanatory hypotheses can carry truth degrees rather than binary values; an observation might have a higher degree than its explanation. This nuance allows models to express uncertainty about real-world events. ¹

To formalize these settings they employ infinitely-valued Łukasiewicz fuzzy logic whose semantics are defined over the continuous interval. Within this system 0 denotes absolute falsity, 1 denotes absolute truth, and intermediate numbers represent graded truth. ¹

They consider two standard entailment relations for Ł: the ‘truth-preserving’ relation, which requires that if a premise is absolutely true then any conclusion derived from it must also be absolutely true, and the ‘degree-preserving’ relation, which demands that the truth degree of a premise never exceed that of the conclusion. Both provide different logical guarantees when combining premises with potential explanations. ¹

For each entailment relation the paper defines notions of abduction problems and corresponding explanations in the language of Ł extended by interval literals of the form p ≥ c, p ≤ c, and their negations. These constraints allow statements such as “the lift’s load is at least 70%.” By embedding such constraints into abductive reasoning, the authors can generate hypotheses that respect both observed degrees and specified bounds. ¹

The study contributes a formal bridge between fuzzy logic and abductive inference, offering a principled way to handle partial truths in automated reasoning systems. It opens avenues for future work on integrating graded knowledge bases with machine learning models that must reason under uncertainty. ¹